3.3, 3.6 prove theorems about perpendicular lines
TRANSCRIPT
Proving Conditional Statements (if-then)Name Math Statement True/False
Conditional P → Q If a set of angles are a linear pair, then they are supplementary
True
Converse Q → P If a set of angles are supplementary, then they are a linear pair.
False
Inverse ~P →~Q If a set of angles are not a linear pair, then they are not supplementary
False
Contrapositive ~Q →~P If a set of angles are not supplementary, then they are not a linear pair.
True
Biconditional P↔Q A set of angles are a linear pair IFF they are supplementary
FALSE since Conditional and Converse not both true
If I know corresponding and alternate interior/exterior angles are congruent , I can prove lines are parallel.
Theorems/Postulates CONVERSE
• Converse of Corresponding Angles Postulate:– If 2 lines are cut by a transversal, and a pair of
corresponding angles are congruent, then the 2 lines are parallel
• THEOREMS: If two lines are cut by a transversal and a pair of– alternate interior angles are congruent, then the
lines are parallel– alternate exterior angles are congruent, then the
lines are parallel– consecutive interior angles are supplementary,
then the lines are parallel
Conclusion:Two lines are cut by a transversal. How can you prove the
lines are parallel?
Show that either a pair of alternate interior angles, a pair of corresponding angles, or a pair of alternate exterior angles is congruent, or show that a pair of consecutive interior angles is supplementary.
Write 3 bi-conditional Statements using the theorems we discussed today
Coordinate Proof• 1) Prove that quadrilateral A(1,2), B(2,5),
C(5,7) and D(4,4) is a parallelogram by using slopes.
• Prove that A(1,1), B(4,4), C(6,2) are the vertices of a right triangle.
• 5) Prove that A(-3,2), B(-2,6), C(2,7)and D(1,3) is a rhombus.
• Prove that A(4,-1), B(5,6), C(1,3) is an isosceles right triangle.
Perpendicular Discussion
• Perpendicular and Linear Pairs
• Perpendicular Lines and Angles Formed
• Adjacent Acute Angles and Perpendicular Lines
• Transversal perpendicular to 1 line in a set of parallel lines
• Lines perpendicular to the same line